South Carolina Highway Patrol Corporal Bill Rhyne said Chapman was driving a Ford Explorer on Highway 23 in Edgefield when he ran off the left shoulder, overturning his vehicle around 10:15 p.m. Friday.
Chapman was transported to the Medical College of Georgia where he later died.
Officials are unsure if the officer was wearing a seatbelt at the time of the accident.
The crash is still under investigation by the South Carolina Highway Patrol.
Summerville Police wrote, "Our thoughts and prayers are with his family and agency during this difficult time."